z=cos(4 theta)

Question

what is the derivative.

I know that the derivative of cos is -sin, but what do i do with the 4 theta. does that just become 4?

Answer 1

dz/d(theta) = -sin(4theta) * 4
= -4sin(4theta)

in general if
y = cos u
then dy/dx = -sin u (du/dx)